The invention relates in general to munitions and in particular to large gun barrels or tubes.
Due to the unavoidable presence of residual stress in the manufacture of gun barrels, it is virtually impossible to produce a gun barrel that is adequately straight, without post-machining straightening. The process of barrel straightening involves physically altering the residual stress distribution in the barrel by some means, such as bending the barrel beyond the elastic limit of the barrel material in a press. The straightening process requires as input some description of the state of the barrel centerline as manufactured.
A known method first establishes a reference line between the centers of the bore at the breech and muzzle ends of the barrel. The reference line may comprise a taut wire or a laser beam. A target, constrained by the barrel bore so that the target center is collocated with the centerline of the bore, is then moved from station to station (axially) along the tube. By using a telescope to view the target calibration with respect to the reference centerline, a table of offsets of the centerline curve can be created. Based only on the table of offsets and his experience, the operator of the straightening press must produce as straight a tube as possible. The lack of further guidance in this process makes it very much a matter of the operator's skill.
To improve productivity and quality, a more accurate and complete description of the barrel centerline curve is required. Specifically, if the magnitude and the point of application of the corrective bending moment are to be directly calculated rather than estimated by the press operator, then the curvature of the barrel centerline must be precisely known. The curvature of the barrel centerline at stations along the length of the barrel may be obtained using the curvature formula. The curvature formula is solely a function of the first and second derivatives of the centerline curve. Because the centerline curve for a particular barrel is not a known mathematical function, its derivatives must be determined numerically.
In theory, it may be possible to calculate the required derivatives using the offsets of the centerline curve as measured by the known method discussed above. However, the calculation of numerical derivatives is a process that is inherently unstable. That is, unlike numerical integration and, depending on the precision of the measurements used, a decrease in the size of the measurement interval beyond a certain point leads to increased error. Thus, the lack of measurement precision places an absolute limit on the precision of the derivative calculation. Because the measurement of the offsets of the centerline curve by the known method is not very precise, it is problematic, on that basis alone, to base the calculation of the derivatives on such measurements.
Furthermore, because the curvature formula contains second order as well as first order derivatives, an additional source of error exists when using the measured offsets of the centerline curve. The additional error is the accumulating error that occurs with successive numerical operations. There are formulas for calculating higher order derivatives directly, but these formulas are less accurate than the first order derivative formulas. Thus, a need exists for a more accurate method of determining the curvature of a tube.